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Publisher: Cambridge University Press   (Total: 387 journals)

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 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 0      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [387 journals]
• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++${\mathcal{W}}$ ++++++++++++ ++++++++ ++++-algebras&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2019&rft.volume=155&rft.spage=2235&rft.epage=2262&rft.aulast=Arakawa&rft.aufirst=Tomoyuki&rft.au=Tomoyuki+Arakawa&rft.au=Edward+Frenkel&rft_id=info:doi/10.1112/S0010437X19007553">Quantum Langlands duality of representations of ${\mathcal{W}}$ -algebras
• Authors: Tomoyuki Arakawa; Edward Frenkel
Pages: 2235 - 2262
Abstract: We prove duality isomorphisms of certain representations of ${\mathcal{W}}$ -algebras which play an essential role in the quantum geometric Langlands program and some related results.
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007553
Issue No: Vol. 155, No. 12 (2019)

• Laurent phenomenon and simple modules of quiver Hecke algebras
• Authors: Masaki Kashiwara; Myungho Kim
Pages: 2263 - 2295
Abstract: In this paper we study consequences of the results of Kang et al. [Monoidal categorification of cluster algebras, J. Amer. Math. Soc. 31 (2018), 349–426] on a monoidal categorification of the unipotent quantum coordinate ring $A_{q}(\mathfrak{n}(w))$ together with the Laurent phenomenon of cluster algebras. We show that if a simple module $S$ in the category ${\mathcal{C}}_{w}$ strongly commutes with all the cluster variables in a cluster $[\mathscr{C}]$ , then $[S]$ is a cluster monomial in $[\mathscr{C}]$ . If $S$ strongly commutes with cluster variables except for exactly one cluster variable $[M_{k}]$ , then $[S]$ is either a cluster monomial in $[\mathscr{C}]$ or a cluster monomial in
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007565
Issue No: Vol. 155, No. 12 (2019)

• Bounding the covolume of lattices in products
• Authors: Pierre-Emmanuel Caprace; Adrien Le Boudec
Pages: 2296 - 2333
Abstract: We study lattices in a product $G=G_{1}\times \cdots \times G_{n}$ of non-discrete, compactly generated, totally disconnected locally compact (tdlc) groups. We assume that each factor is quasi just-non-compact, meaning that $G_{i}$ is non-compact and every closed normal subgroup of $G_{i}$ is discrete or cocompact (e.g.  $G_{i}$ is topologically simple). We show that the set of discrete subgroups of $G$ containing a fixed cocompact lattice $\unicode[STIX]{x1D6E4}$ with dense projections is finite. The same result holds if $\unicode[STIX]{x1D6E4}$ is non-uniform, provided $G$ has Kazhdan’s property (T). We show that for any compact subset $K\subset G$ , the collection of discrete subgroups $\unicode[STIX]{x1D6E4}\leqslant G$ with
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007644
Issue No: Vol. 155, No. 12 (2019)

• Compatible systems and ramification
• Authors: Qing Lu; Weizhe Zheng
Pages: 2334 - 2353
Abstract: We show that compatible systems of $\ell$ -adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite field. As an application, we deduce the equicharacteristic case of classical conjectures on $\ell$ -independence for proper smooth varieties over complete discrete valuation fields. Moreover, we show that compatible systems have compatible ramification. We also prove an analogue for integrality along the boundary.
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007619
Issue No: Vol. 155, No. 12 (2019)

• On Selberg’s eigenvalue conjecture for moduli spaces of abelian
differentials
• Authors: Michael Magee
Pages: 2354 - 2398
Abstract: J.-C. Yoccoz proposed a natural extension of Selberg’s eigenvalue conjecture to moduli spaces of abelian differentials. We prove an approximation to this conjecture. This gives a qualitative generalization of Selberg’s $\frac{3}{16}$ theorem to moduli spaces of abelian differentials on surfaces of genus ${\geqslant}2$ .
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X1900767X
Issue No: Vol. 155, No. 12 (2019)

• Patching over Berkovich curves and quadratic forms
• Authors: Vlerë Mehmeti
Pages: 2399 - 2438
Abstract: We extend field patching to the setting of Berkovich analytic geometry and use it to prove a local–global principle over function fields of analytic curves with respect to completions. In the context of quadratic forms, we combine it with sufficient conditions for local isotropy over a Berkovich curve to obtain applications on the $u$ -invariant. The patching method we adapt was introduced by Harbater and Hartmann [Patching over fields, Israel J. Math. 176 (2010), 61–107] and further developed by these two authors and Krashen [Applications of patching to quadratic forms and central simple algebras, Invent. Math. 178 (2009), 231–263]. The results presented in this paper generalize those of Harbater, Hartmann, and Krashen [Applications of patching to quadratic forms and central simple algebras, Invent. Math. 178 (2009), 231–263] on the local–global principle and quadratic forms.
PubDate: 2019-12-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007632
Issue No: Vol. 155, No. 12 (2019)

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